Exploding solitons and Shil'nikov's theorem

Nail Akhmediev; J. M. Soto-Crespo

doi:10.1016/j.physleta.2003.08.060

Exploding solitons and Shil'nikov's theorem

Nail Akhmediev^*
, J. M. Soto-Crespo

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

54 Citations (Scopus)

Abstract

We have performed a detailed linear stability analysis of exploding solitons of the complex cubic-quintic Ginzburg-Landau (CGLE) equation. We have found, numerically, the whole set of perturbation eigenvalues for these solitons. We propose a scenario of soliton evolution based on this spectrum of eigenvalues. We relate exploding and self-restoring behavior of solitons to the Shil'nikov theorem, and point out common features and differences between our system, with an infinite number of degrees of freedom, and Shil'nikov's system with three degrees of freedom.

Original language	English
Pages (from-to)	287-292
Number of pages	6
Journal	Physics Letters, Section A: General, Atomic and Solid State Physics
Volume	317
Issue number	3-4
DOIs	https://doi.org/10.1016/j.physleta.2003.08.060
Publication status	Published - 20 Oct 2003

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10.1016/j.physleta.2003.08.060

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title = "Exploding solitons and Shil'nikov's theorem",

abstract = "We have performed a detailed linear stability analysis of exploding solitons of the complex cubic-quintic Ginzburg-Landau (CGLE) equation. We have found, numerically, the whole set of perturbation eigenvalues for these solitons. We propose a scenario of soliton evolution based on this spectrum of eigenvalues. We relate exploding and self-restoring behavior of solitons to the Shil'nikov theorem, and point out common features and differences between our system, with an infinite number of degrees of freedom, and Shil'nikov's system with three degrees of freedom.",

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T1 - Exploding solitons and Shil'nikov's theorem

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AU - Soto-Crespo, J. M.

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Y1 - 2003/10/20

N2 - We have performed a detailed linear stability analysis of exploding solitons of the complex cubic-quintic Ginzburg-Landau (CGLE) equation. We have found, numerically, the whole set of perturbation eigenvalues for these solitons. We propose a scenario of soliton evolution based on this spectrum of eigenvalues. We relate exploding and self-restoring behavior of solitons to the Shil'nikov theorem, and point out common features and differences between our system, with an infinite number of degrees of freedom, and Shil'nikov's system with three degrees of freedom.

AB - We have performed a detailed linear stability analysis of exploding solitons of the complex cubic-quintic Ginzburg-Landau (CGLE) equation. We have found, numerically, the whole set of perturbation eigenvalues for these solitons. We propose a scenario of soliton evolution based on this spectrum of eigenvalues. We relate exploding and self-restoring behavior of solitons to the Shil'nikov theorem, and point out common features and differences between our system, with an infinite number of degrees of freedom, and Shil'nikov's system with three degrees of freedom.

KW - Complex Ginzburg-Landau equation

KW - Dissipative solitons

UR - https://www.scopus.com/pages/publications/0142059923

U2 - 10.1016/j.physleta.2003.08.060

DO - 10.1016/j.physleta.2003.08.060

M3 - Article

SN - 0375-9601

VL - 317

SP - 287

EP - 292

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 3-4

ER -

Exploding solitons and Shil'nikov's theorem

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